Toyosi arrived late, --------------- the right route

Analyze the question: The sentence is "Toyosi arrived late, __ the right route." The gap needs a verb form that explains why she was late. The logical meaning is that she probably did not take the right route, so we need a modal perfect (a modal verb plus have plus the past participle) to express a past deduction.

Concept: To make a deduction or guess about a past event, we use:

modal (could / must / might / cannot) + have + past participle

• Example: He could not have seen me.
• The past participle of "take" is taken, not "take" or "took".

Checking each option:

• A. Cannot have taken – The form is grammatical. However, "cannot" is present tense and does not fit well with the past-tense narration ("arrived"). It also gives the wrong meaning here, since "cannot have taken the right route" would be a firm conclusion rather than a matching past-tense expression. The sequence of tenses points to "could".
• B. Could not have take – Wrong, because "take" should be the past participle "taken".
• C. could not had taken – Wrong, because after a modal we use "have", not "had".
• D. could not have taken – Correct. The modal is past (could), followed by "have" and the past participle "taken".

Full sentence: Toyosi arrived late, could not have taken the right route. In standard written English a connecting word or comma structure would normally be used, but among the options, D is the only one that is both grammatically correct and consistent in tense with "arrived".

Note: the sentence as printed is a bit awkward, and the meaning could even be read as "she arrived late because she did not take the right route".

Exam tip: Remember the formula modal + have + past participle. Whenever you see "could/should/would/must/might + ___", check two things: that "have" (not "had" or "has") follows the modal, and that the main verb is in its past participle form (taken, seen, gone, written).